Bullish investors are starting to believe that the US stock markets are going to turn around.

Fundstrat's Tom Lee believes that the summer rally on the major US benchmarks is a sign that the stock market will hit all-time highs by the end of the year.

Over the past two months, the S&P 500 and the tech-laden Nasdaq have gained 20% and 20%, respectively. The Federal Reserve's pledge to be data dependent on interest rate hikes and a lower-than- expected July inflation print have given traders reason for optimism.

Wall Street's biggest names don't think it's true. The current rebound in stocks is just a classic bear market rally, according to analysts at big banks.

Despite the bear market, stock prices are still not cheap, according to a recent research note.

After the S&P 500's rally from its June low, they are more expensive.

It's not the right time for investors to try to time the bottom, as disappointing economic data could push stocks lower, according to analysts.

The head of Americas asset allocations at the Swiss bank said that becoming more optimistic in the current highly uncertain environment makes the markets more vulnerable to negative news.

The base case of Wall Street is that stocks will not stage a true revival until the Fed starts cutting interest rates. The US central bank raised rates by 75 basis points in June and July in order to tame inflation.

Mike Wilson told investors not to bet on a rate-hike pause. July's strong labor market report, which showed the US adding 528,000 jobs, gave the Fed scope to continue raising interest rates.

"While inflation appears to be peaking, it's not likely to come off at a pace fast enough to spur the type of sustained Fed pause the equity market is already discounting," said Wilson.

Bank of America said this week that it expects rate hikes to continue until February 23,23, when nominal interest rates will hit 4%. Goldman said the Fed's pause would only happen at the end of the year.

Wall Street doesn't think it's a good idea for investors to buy indiscriminately in the equity markets.

Wilson said that the message from them remained. The bear market is incomplete due to the unattractive risk/reward.

Morgan Stanley says investors shouldn't be fooled by the bear market rally, but they should buy 22 stocks that will beat the S&P 500.